In the field of geotechnical engineering, instruments called inclinometers are available for measuring tilt in vertical or horizontal boreholes, for the purpose of calculating a path of the borehole based on one- or two-degree-of-freedom tilts, the length of the inclinometer, and the known orientation of the inclinometer about its long axis, which is controlled by straight grooves in the inclinometer casing lining the borehole. The inclinometer is either moved along the casing and stopped at spatial intervals for reading tilt (traversing inclinometer), or multiple inclinometers rest in the casing and are read at intervals in time (in-place inclinometers). Traversing inclinometers and in-place inclinometers will be referred to here as “conventional inclinometers”.
An improvement over in-place inclinometers has been patented (Danisch '363). It is a calibrated measurement instrument comprised of rigid tubes (rigid bodies) fitted with tilt sensors, the tubes separated by built-in bendable joints resistant to twist, that can be used directly without grooved casing to measure path shape and vibration along the path. Danisch '363 will be referred to hereinafter as “SAA”, or ShapeAccelArray. The SAA does not require grooves in the casing to perform azimuthal alignment of each rigid body about the long axis of the SAA. The twist-resistant joints maintain azimuthal alignment. Azimuth of each rigid body, which is not physically controlled during manufacture, is calibrated at the end of the manufacturing process, by using the X and Y tilt sensors in each body to measure the “roll” angle of each body when the SAA is generally horizontal. During manufacture, all offsets and gains of the sensors are calibrated so that accurate tilt measurements can be made over a wide temperature range, and over all angles.
Both conventional inclinometers and SAA rely on gravimetric measurement of tilt. Measurement of tilt amounts to determining the portion of the gravity vector acting upon a mass supported by springs in a reference frame, as the axis of the reference frame is tilted. In some cases, conventional inclinometers use liquid-filled curved tubes instead of springs and masses. In other cases, servo-controlled springs and masses are used.
Calculation of shape from tilts is known from the prior art. In general, an array of rigid bodies separated by flexible joints can be portrayed as a polyline (line segments meeting at vertices), whose vertices represent the joint centers. Lengths of the line segments are usually taken to be the joint-center to joint-center distance when the array is straight. For a vertical array extending in Z, and bending in X and Y, X and Y tilt sensors are sufficient to sense the overall tilts of the rigid bodies. The Z sensor is needed only to report if the array is “upside down” or not. It is essential to constrain the joints to have either 1DOF of bend and 1DOF of twist, or 2DOF of bend without twist, or the azimuths of the X and Y sensors within the World Coordinate System (WCS) will not be known. With the joint constraint, it is possible to solve for X and Y tilts and to know their azimuth (compass) directions, even far from a reference end for the calculation. Constraint in inclinometer systems is provided by grooves in the inclinometer casing. The rigid bodies of inclinometers have wheels that fit into the grooves. For SAA, the joints are built to resist twist but permit 2DOF bend, or for ribbon-shaped forms of SAA, the joints have 1DOF of bend and 1DOF of twist. The constraint allows calculation of the 2DOF orientation of each segment relative to the one before, based on X and Y tilts.
Calculation of shape for horizontal prior-art straight arrays is limited to shape within a vertical plane containing the path of the array. Only the Z sensors are needed.
Deficiencies of conventional inclinometers include:                Traversing inclinometers (individual instruments lowered and read at intervals) must be read by a person at the site, so automated data collection at frequent intervals is not possible.        In-place inclinometer systems have multiple inclinometers connected as a chain, each inclinometer having wheels that fit into grooves in inclinometer casing. The “gauge length” of each individual inclinometer (an inclinometer is a rigid body) can be extended by means of a rigid rod with one of the wheel assemblies at its end. The installer must keep track of the order of inclinometers, their lengths, and their calibration coefficients. In-place inclinometer systems are known to be difficult to install and are often limited in length by the number of cables which must pass to the surface from each inclinometer. The cable problem can be circumvented by digitizing and using a common serial “bus cable”, but at higher cost and still with the complexity of wheels and grooves.        Long gauge lengths lead to easy distortion or entrapment of in-place inclinometers even for small deformations, leading to loss of equipment and money.        Inclinometers use grooved casing to keep the axes of the inclinometers aligned to an azimuth. This precludes using stiff, thick metal tubes instead of the inclinometer casing, to provide protection. Wheels would have difficulty passing joints between sections of robust tubing.        
Deficiencies of SAA include:                Although SAA is convenient because it is a calibrated, self-contained array that is stored on a reel, it is limited to short gauge lengths (lengths of its rigid bodies) because a very large reel would be required, and the small size of the casing in which it is installed would cause bending of its rigid bodies at very small deformations. The short segments must all have sensors, or information would be lost along the array. For example, if a narrow shear zone in the soil happens to tilt only one rigid body, with the other rigid bodies remaining upright, large errors would occur if the one tilted body had no sensors. The requirement for many short rigid bodies leads to higher cost.        Often construction sites are not expected to involve large deformations. It is sufficient to get a warning during the low-magnitude early phases of deformation. SAA has too many sensors and therefore too high a cost, for these situations, so its convenience in many construction monitoring applications is not always sufficient to justify its price.        
Deficiencies of both in-place inclinometers and SAA include:                Neither type of instrument is armored to withstand crushing by rocky soil or pure rock formations. There is only plastic casing and a small amount of air between the delicate instrument and the outside medium.        Neither type of instrument can be retrieved from a casing that has been greatly deformed. There is insufficient room for either instrument to negotiate sharp curves or other deformations of the casing.        
Prior-art inclinometers and SAA do not provide a convenient, no-wheels array that fits on a reel and is a self-contained, calibrated instrument not requiring special grooved casing, while simultaneously providing a means of having long rigid-body lengths upon installation.
Prior-art inclinometers with long gauge lengths in large-diameter casing, and SAA with short gauge lengths in small-diameter casing, do not provide for extracting the instruments after deformation has curved the borehole, by allowing a separate instrumented array having short rigid bodies to be pulled out of a sacrificial set of longer rigid bodies left in the borehole.
Prior-art inclinometers and SAA do not provide for longevity in rocky soils, by having robust outermost rigid bodies connected by bendable joints, the rigid bodies providing protection of internal, less robust rigid bodies, from rock forces.
Prior-art inclinometers and SAA do not provide for a very flexible array made of rigid bodies connected by flexures long enough to allow positional displacement, deployable from a reel, contained by a separate system of longer rigid bodies with joints providing bending without shear (i.e. preventing unmeasured lateral positional displacement of the contained inner array).
Prior-art inclinometers and SAA do not provide for a system of hollow rigid bodies and joints (“second hollow exoskeleton portion”), without sensors, that can be supplied locally from a variety of materials, and installed prior to arrival of a “second sensorized array portion” that fits inside, the two systems then working together to provide measurements of shape and deformation of shape, the sensorized portion being low in cost due to large spacing of sensors.
Related to the helical forms for some of the paths of the bipartite array components described herein, prior-art inventions have included non-straight sensor paths, but have relied on bend and twist sensors (“curvature” sensors). For instance Danisch '107 (“Shape Rope”) describes                “A measuring device for providing data corresponding to a geometric configuration in space, in the form of a flexible, compliant, measurement member capable of bending in at least one degree of freedom and extending along a medial axis or plane. The member has spaced flexure sensors distributed at known locations on the member and separated by known sensor spacing intervals to provide flexure signals indicating the local state of flexure present at the locations. The member comprises a multiplicity of formed, i.e. shaped, fibers, these fibers including sensing fibers having sensing portions which provide the flexure sensors, the sensing portions of different fibers being located at differing distances along the member so as to be located at the sensor spacing intervals, the formed fibers being in mutually supporting relationship, as by continuous or repeated contact with each other. Such fibers may constitute most or all of the member”.        
Devices using flexural sensors in concatenated arrays suffer from a serious deficiency: when there is an error in one of the sensors, the orientation of all of the array past that point in the order of calculation will share the angular offset of the error, which will cause the entire data set representing a measured path to swing well away from the path, by the angle of the error. This can result in a huge displacement at the end of the path.
Further, in Danisch '107 the fibers are pre-formed and in a mutually-supporting relationship that is not suited to being compressed axially and thereby swelling laterally to conform to an enclosing surface. Danisch '107 does not teach a straight array that may be rolled up onto a reel that can be deployed straight, and then formed into a helix by inserting it into a hollow exoskeleton portion and applying axial compressive force for secure containment. Instead, Danisch '107 requires that a multiplicity of fibers be pre-formed into mutually-supporting helices of fixed dimensions, the configuration not being amenable to the use of gravitational sensors measuring tilt. There is no teaching of rigid bodies separated by flexible joints, the rigid bodies providing a means of sampling tilt uniformly along a region, referenced to gravity, rather than sampling bend along a flexible member easily distorted by contact with objects. There is no teaching of flexible joints providing torsional stiffness but allowing bend, between rigid bodies. There is no teaching of referencing all the sensors to gravity, so that orientation errors cannot propagate up a calculation chain. There is no teaching of sensors in rigid bodies so that orientation may be read directly by gravimetric sensors, rather than inferred from measurements of bend and twist. Furthermore, there is no inclusion of a second hollow exoskeleton portion containing a first sensory array portion, thus providing advantages of protection of the first portion, reduction in the number of sensors, provision of long gauge lengths, and separate manufacture, supply, delivery, and installation of a second hollow exoskeleton portion.
Although 3D measurements can be made with bend and twist sensors over a full spherical range of orientations, the accuracy of bend and twist sensors excludes them from use for monitoring geotechnical parameters. Geotechnical measurements must be accurate to one or two millimeters over array lengths of tens of meters, for decades. Practical, low-cost bend and twist sensors, such as the fiber optic curvature sensors used in the Danisch '107 and '672 prior art, are not capable of such accuracy. They are capable of approximately 1 cm per meter, per day, which is orders of magnitude too poor for geotechnical measurements.
Danisch '672 (“Shape Tape”), which describes                “A position, orientation, shape and motion measuring tool is provided in the form of a flexible substrate with bend and twist sensors distributed along its surface at known intervals. A ribbon-type substrate is preferred. The geometric configuration of the substrate is calculated from inter-referencing the locations and orientations of the sensors based upon the detected bend and twist values. Suitable applications include motion capture for humans for use in animation, six degree of freedom input to a computer, profile measurement and location tracking within a large, singularity-free working space”.is not amenable to installation in hollow tubes for measuring 3D shape, as “Shape Tape” cannot bend within its plane, and would not respond well (it could buckle or break) to deformations of a hollow exoskeleton portion imposing such bends on its ribbon form. Nor does it teach use of gravimetric sensors for increased accuracy, as discussed above for Danisch '107.        
None of Danisch '672, '107, or '363, nor prior-art inclinometry teach the securing of an array within a surface by means of lateral expansion caused by axial compression of the form of the array. Neither does any of the prior art provide a means of protecting arrays from external forces while maintaining good flexibility, by means of a hollow exoskeleton portion, or of using the same hollow exoskeleton portion to achieve long gauge lengths.